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Re: - FFT and Mathematica

On Sat, 8 Apr 1995 David E. Burmaster:

> Dear MathGroupers
> Can someone pls recommend a book or an article that discusses how to use
> FFT in Mathematica?? ..... hopefully  something with lots of examples,
> including convolutions  done using FFTs....
> Thank you for your help......
> Dave
> David E. Burmaster

Dear Dave,

I recommend you the book: Richard E. Crandall, "Projects in Scientific
Computation", Springer-Verlag, New York, 1994. This book is about computation
in many fields, but there is a paragraph (4th) about FFT (pages 151 - 195). For
this book is a floppy disk included with the examples in two formats:
Mathematica Notebook or C source code.

It is a short list of this paragraph:

4. The FFT forest. The ubiquitous FFT and its relatives.
4.1 Discrete Fourier transform
4.1.1 Fundamental DFT manipulations
4.1.2 Algebraic aspects of the DFT
4.1.3 DFT test signals (+ "" mma notebook file)
4.1.4 DFT software (+ "fft.c" C source code file)
4.2 FFT algorithms
4.2.1 Recursive FFTs (+ " mma notebook file)
4.2.2 FFT indexing and butterflies
4.2.3 Complex FFTs, N a power of 2 (+ "" mma notebook file)
4.2.4 Real-signal FFTs (+ "fft_real.c C source code file)
4.2.5 FFTs for other radices
4.2.6 FFTs in higher dimensions
4.2.7 Applications of the FFT
4.3 Real-valued transforms
4.3.1 Hartley transform (+ "" mma notebook file)
4.3.2 Discrete cosine transform
4.3.3 Walsh-Hadamard transform (+ "walsh.c" C source code file)
4.3.4 Square-wave transform (+ "" mma notebook file)
4.4 Number-theoretic transforms
4.4.1 Exploring Number-theoretic transforms

If you want I can send to you these source text files. 
It is a fragment of "prohibitions" from "readme" file included with the book:

"[...] This electronic component package is protected by federal copyright law
and international treaty. The copyright holder retains title to and ownership
of the package. US copyright law prohibits you from making any copy of the 
diskette for any reason, without the written permission of Springer-Verlag, 
except that you may download and copy the "readme" and source text files for 
your own research, teaching, and personal communications use. [...]
The printed book with which this electronic component is packaged may not be 
translated or copied in whole or in part without the written permission of 
Springer-Verlag except for brief excerpts in connection with reviews or 
scholarly analysis. [...]"

The other source may be a Signal Processing Packages and Notebooks, it is
"a hierarchical set of packages to perform basic analyses of signals (functions)
and systems (operators). The packages are based on transform theory and
implement many concepts from linear transform theory. They support (bilateral)
z- and Laplace transforms, as well as continous-time, discrete-time, and
discrete Fourier transforms, all in arbitrary dimension. [...]"

This package is available for DOS, Unix and Macintosh systems by ftp from
MathSource (, item No. 0202-240, or from, Mathematica directory.

Hope this help, Grzegorz.

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